ADMISSIBILITY OF LIKELIHOOD RATIO RULES IN COVARIATE CLASSIFICATION USING DEPENDENT SAMPLES

The two populations considered for this study are two distinct time points. Samples consist of observations made at both the time points on every sampling unit. The unit to be classified is observed at one of the two time points. The observation vectors contain covariates, having same expectation at both the time points. In this set-up admissibility of some likelihood ratio rules is established.     

CLASSIFICATION, DISTRIBUTIONS AND ADMISSIBILITY IN AUTOREGRESSIVE PROCESS

The problem considered here is to classify a unit into one of two populations based on a vector of measurements on the unit. The observation vector is assumed to follow an auto-regressive process. Samples from the process are used to construct classification rules. The distributions of some classification statistics are obtained. The admissibility of some classification rules is established.     

Two population classification in Gaussian process

The problem is to classify an individual into one of two populations based on an observation on the individual which follows a stationary Gaussian process and the populations are two distinct time points. Plug-in likelihood ratio rules are considered using samples from the process. The distribution of associated classification statistics are derived. For the special case when the mis-classification probabilities are equal, the nature of dependence between the population distributions on the probability of correct classification is studied. Lower bounds and iterative method of evaluation of the optimal correlation between the populations are obtained.     

Covariate Classification Using Dependent Samples

The two-population classification problem using dependent samples is extended when covariates are available for classification. Analysis is done using a conditional model, under a multivariate normal set-up, given the covariates. The conditional model considered here includes the parameter structure relevant to growth models. Likelihood ratio or plug-in likelihood ratio classification rules are derived depending on the knowledge of the parameters in the model. For exact distribution of the classification statistics, they are reduced to forms suitable for application of standard results.     

Sampling strategy for optimal classification into one of two correlated normal populations

A unit ω is to be classified into one of two correlated homoskedastic normal populations by linear discriminant function known as W classification statistic [T.W. Anderson, An asymptotic expansion of the distribution of studentized classification statistic, Ann. Statist. 1 (1973), pp. 964–972; T.W. Anderson, An Introduction to Multivariate Statistical Analysis, 2nd edn, Wiley, New York, 1984; G.J. Mclachlan, Discriminant Analysis and Statistical Pattern Recognition, John Wiley and Sons, New York, 1992]. The two populations studied here are two different states of the same population, like two different states of a disease where the population is the population of diseased patient. When a sample unit is observed in both the states (populations), the observations made on it (which form a pair) become correlated. A training sample is unbalanced when not all sample units are observed in both the states. Paired and also unbalanced samples are natural in studies related to correlated populations. S. Bandyopadhyay and S. Bandyopadhyay [Choosing better training sample for classifying an individual into one of two correlated normal populations, Calcutta Statist. Assoc. Bull. 54(215–216) (2003), pp. 167–180] studied the effect of unbalanced training sample structure on the performance of W statistics in the univariate correlated normal set-up for finding optimal sampling strategy for a better classification rate. In this study, the results are extended to the multivariate case with discussion on application in real scenario.